Kasparov KK-groups KK(A,B) are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic K-theory spectrum of the additive category of Fredholm (A,B)-bimodules for A and B, respectively, a separable and σ-unital trivially graded real or complex C∗-algebra acted upon by a fixed compact metrizable group.

Let p be a prime number. In [9], I introduced the Roquette category Rp of finite p-groups, which is an additive tensor category containing all finite p-groups among its objects. In Rp, every finite p-group P admits a canonical direct summand ∂P , called the edge of P . Moreover P splits uniquely as a direct sum of edges of Roquette p-groups. In this note, I would like to describe a fast algorit...

Category ranking is the task of ordering labels with respect to their relevance to an input instance. In this paper we describe and analyze several algorithms for online category ranking where the instances are revealed in a sequential manner. We describe additive and multiplicative updates which constitute the core of the learning algorithms. The updates are derived by casting a constrained op...

The theorem of the title is deduced from the equivalence between crossed complexes and cubical ω-groupoids with connections proved by the authors in 1981. In fact we prove the equivalence of five categories defined internally to an additive category with kernels.

Humans are remarkably efficient in detecting highly familiar object categories in natural scenes, with evidence suggesting that such object detection can be performed in the (near) absence of attention. Here we systematically explored the influences of both spatial attention and category-based attention on the accuracy of object detection in natural scenes. Manipulating both types of attention ...

In this paper, we further explore the conceptual approach to cyclic cohomology with coefficients initiated in [HKS]. In particular we give a derived version of the definition with better invariance properties. We show that the new definition agrees with the old under certain conditions and we prove, for the new definition, both its Morita invariance and its 2-Morita invariance, under suitable i...

Our purpose here is to obtain intrinsic functorial characterizations of the functors Horn and ® and thus to account in part for the distinguished role played by then in homological algebra. In all that follows, A, r are rings with unit, Z the ring of integers. The category of all T-A-bimodules with F operating on the left, A on the right, is denoted by tSIZa, the category of left A-modules (T-m...

Dedicated to the memory of Maurice Auslander Given a ring we introduce the endocategory E M of a-module M. It is an abelian subcategory of Mod(?) where ? = End (M) op , and E M is constructed in such a way that it is the smallest abelian subcategory of Mod(?) containing M regarded in the natural way as a ?-module and all the endomorphisms of M induced by multiplication with an element from. The...

Let a compact group G act on real or complex C∗-algebras A and B, with A separable and B σ-unital. We express the G-equivariant Kasparov groups KKn(A,B) by algebraic K-groups of a certain additive category.

We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we prove that every simple transitive 2-representation of the 2-category of projective bimodules over a finite dimensional algebra is equivalent to a cell 2-representation.